A constitution disclosed in, for example, Patent Document 1 is known as such a type of vibration damping device. Such a vibration damping device includes a first tubular attachment member coupled to one of a vibration-generating part and a vibration-receiving part, a second attachment coupled to the other part, an elastic body coupling the attachment members to each other, and partition members configured to partition a liquid chamber in the first attachment member in which a liquid is sealed in a first liquid chamber and a second liquid chamber. The vibration damping device further includes a first restriction passage and a second restriction passage which communicate the liquid chambers with each other, a cylinder chamber provided between the liquid chambers, and a plunger member arranged movably between an open position and a closed position in the cylinder chamber.
A plurality of types of vibrations with different frequencies such as, for example, an idle vibration and a shake vibration are input to the vibration damping device. Resonance frequencies of the first restriction passage and the second restriction passage are set (tuned) to frequencies of the different types of vibrations in the vibration damping device. The plunger member is moved between the open position and the closed position according to frequencies of the input vibrations so that a restriction passage through which the liquid flows is switched between the first restriction passage and the second restriction passage.